
Each set of parameters \(\lbrace \gamma , b_2 , b_4 , b_6 \rbrace \)  leads to a black hole solution. This family of black hole solutions has been introduced in [1]}, [2]} and used to mimic the equation of state of QCD. For small \(\phi \) , one can expand \(V(\phi )\)  as follows
\(V(\phi )\sim -12+ \frac{1}{2}m^2\phi ^2 +\mathcal {O}(\phi ^4),\) 
